1. Field of the Invention
The present invention relates to an induction motor drive, and more particularly, to a vector control of an induction motor.
2. Description of the Related Art
A typical direct field-oriented based induction motor drive system is shown in FIG. 12.
The vector control of an induction motor is performed by adjusting the torque and magnetic flux of an induction motor 102 fed by an inverter 101.
FIG. 12 exemplifies an induction motor drive comprising a speed sensor 132. With the vector control of this system, a speed regulator 105 generates a torque current reference 114 based on a PI (Proportional action and Integral action) control from a speed reference 103 being an instruction to the speed of the motor and a rotation speed 112 of the induction motor 102, which is detected by the speed sensor 132 as feedback, and outputs the generated torque current reference 114 to a current regulator 104. The current regulator 104 generates and outputs currents, which are adjusted based on the PI control, from the torque current reference 114 being an instruction to the torque and a flux current reference 113 being an instruction to the flux. Then, a vector rotator 106 transforms these current values into a relative value in a coordinate system (d-q coordinate system) which rotates synchronously with the synthetic vector of the currents, and applies the transformed value to an inverter 101 as a primary voltage command 120. Note that the flux current reference 113 applied to the current regulator 104 can be set constant in a wide range of operation.
Sensors 130 and 131 respectively detect the voltage value and the current value, which are applied from the inverter 101 to the inductor motor 102, as a detected voltage 121 and a detected current 122. After the voltage and the current are transformed into two-phase coordinate system values by 3-2 phase transformers 108 and 109, they are input to a current and flux observer 110 as space vector values Vs 123 and i.sub.s 124.
A stator,rotor resistance (Rs,Rr) estimator 500 estimates a stator resistance Rs and a rotor resistance Rr of the induction motor 102 from the stator current 124 output from the 3-2 phase transformer 109 and an observed current 127 and observed flux 128 output from the current and flux observer 110, and outputs observed values Rs' 503 and Rr' 504 of the resistances Rs and Rr. Then, these values are used by the current and flux observer 110.
The current and flux observer 110 outputs the observed current 127 and the observed flux rotor 128 from the stator voltage Vs 123, the stator current i.sub.s 124, the detected speed 112 of the motor output from the sensor 132, and the estimated stator and rotor resistance values Rs' 503 and Rr' 504 output from the Rs,Rr estimator 500.
The vector rotator 106 vector-rotates the flux command 118 and the torque command 119 in a direction of the flux of the rotor based on the observed rotor flux 128, and outputs the vector-rotated instructions to the inverter 101 as a primary voltage command 120.
Additionally, the vector i.sub.s 124 is vector-rotated by a vector rotator 107 in the direction of the rotor flux based on the observed flux 128 from the current and flux observer 110 in order to obtain the torque current 126 and the flux current 125, which are used as feedback signals by the current regulator 104.
A system without speed sensor, that is a speed-sensorless system, is explained next. In the system comprising no speed sensor, only a stator voltage 121 and a stator current 122 are detected by sensors 130 and 131. The configuration of this system is shown in FIG. 13.
Comparing the configuration shown in FIG. 13 with that shown in FIG. 12, a speed observer 111 which estimates the speed of the motor is added, and an Rs,Rr estimator 501 which estimates resistance values Rs and Rr of the stator and the rotor from a stator current 124, an observed current 127, observed flux 128, and a torque command 119 as a replacement of an Rs, Rr resistance estimator 500.
The speed observer 111 estimates the rotor speed from the stator current i.sub.s 124, the observed current 127 and the observed flux 128 output from a current and flux observer 110, and outputs an observed speed 115 both to a speed regulator 105 and to the current and flux observer 110.
Furthermore, to allow the resistance of the rotor to be observed even in a steady state, a harmonic component 162 is injected in the flux current reference 118.
In the direct field-oriented control, the flux is typically evaluated using an observer as the one described in:
Ref. 1--H. Kubota et al. "Speed Sensorless Field-Oriented Control of Induction Motor with rotor Resistance Adaptation," IEEE Trans. on Ind. Appl., Vol. 30, No. 5, September/October 1994
A conventional mathematical model of the induction motor using a state space notation is as follows: ##EQU1##
The state equation of a simpler observer is represented by the above provided mathematical model (1). This mathematical model is stable, and the following equation for the current and flux observer 110 is derived from this equation. ##EQU2##
where ' indicates an observed value. For example, a matrix A' has the same value as that in the matrix A in the equation (1), but it is evaluated using nominal and estimated parameter values instead of actual values.
The observation and observed values in this specification respectively represent observation and observation values in a modern control theory, and indicates the estimation of state variable values from an output, and the estimated values.
Since the values of the resistances Rs and Rr of the stator and the rotor change with the operating temperature of the motor, their values are normally evaluated during normal motor operations, and the observed values are obtained from the evaluation expression.
This evaluation expression is represented as follows according to the above provided Ref. 1. ##EQU3##
where .multidot. indicates a dot product of vectors, and k1 and k2 are positive constants.
FIG. 14 is a block diagram showing the details of the Rs,Rr estimator 500 of FIG. 12 based on the above described equations (3) and (4).
In the Rs,Rr estimator 500, an observed current i.sub.s ' 127 output from the current and flux observer 110 is first subtracted from the measured current i.sub.s 124 of the stator sensed by the current sensor 131 by a calculator 512 within a stator resistance estimator 502. Next, the dot product of a vector e.sub.is and the observed current i.sub.s ' 127 is obtained by a dot product processor 507, and the obtained dot product by which a constant -k1 is multiplied by a calculator 513 is integrated by an integrator 509. As a result, the integrated value is output as an observed stator resistance Rs'.
In the meantime, the mutual inductance Lm of the induction motor is multiplied by the observed current is' 127 by a calculator 514, and the dot product of the result of the multiplication and the output vector e.sub.is of the calculator 512 is obtained by a dot product processor 508. And a constant k2 is multiplied by the resultant dot product by a calculator 516, and the result of the multiplication is integrated by an integrator 510, so that an observed rotor resistance Rr' 504 is obtained and output.
For a system comprising no speed sensor like the one shown in FIG. 13, a motor rotation speed .omega.r is not measured. Accordingly, its evaluation value .omega.r' 115 is used to evaluate the matrix A' in the equation (2).
The evaluation expression in the speed observer 111 is described as follows. EQU .omega.'.sub.r =(k.sub.P.omega. +s.multidot.k.sub.I.omega.).multidot.((i.sub.sa -i'.sub.sa).multidot..phi.'.sub.r.beta. -(i.sub.s.beta. -i'.sub.s.beta.).multidot..phi.'.sub.ra) (5)
where s is a Laplace operator, and k.sub.P.omega. and k.sub.I.omega. are proper gains. The estimated value Rs' of the stator resistance in the system shown in FIG. 13 is given by the equation (3) in a similar manner as in the system which is shown in FIG. 12 and comprises a speed sensor. In the meantime, the estimated value Rr' of the rotor resistance is given by using an algorithm different from that for the system comprising a speed sensor.
To estimate the resistance Rr on the secondary side, a suitable harmonic signal 162 having a frequency f* is injected in the flux current reference 113 as an injection term. As a result, the equation (4) for the resistance Rr is modified as follows if the system does not comprise a speed sensor. ##EQU4##
where i.sub.d, i.sub.d ', and i.sub.d,ref are respectively the measured value, the observed value, and the reference value of the flux current. Additionally, k3 is a positive constant.
FIG. 15 is a block diagram showing the details of the Rs,Rr estimator 501 of FIG. 13 based on the above provided equations (3) and (6).
The measured current i.sub.s 124 of the stator sensed by the current 131 and the observed current i.sub.s ' 127 from the current and flux observer 110 are respectively vector-rotated by vector rotators 107 and 142 in the direction of the observed flux 128.
After an observed flux current id' 151 is subtracted from the flux current id 125 by the calculator 157, the dot product between the result of the subtraction and the reference value of the flux current is calculated by a dot product processor 517. Then, a constant k3 is multiplied by a calculator 518, and the result of the multiplication is integrated by an integrator 511, so that an observed rotor resistance Rr' 505 is calculated and output.
In the meantime, the observed stator resistance Rs' 503 is calculated from the measured current i.sub.s 124 of the stator and the observed current i.sub.s ' 127 from the current and flux observer 110, and output by the same stator resistance estimator 502 as that shown in FIG. 4.
To precisely control the flux and the torque of the induction motor, the flux direction .phi.r' of the rotor must be accurately observed. However, in the equation (2) for the accurate observation, especially in the matrix A', parameters having the values changing during the operation of the motor, such as the resistance values Rr and Rs on the primary and the secondary sides, which change with a temperature, are included.
The accuracy of the observed values in the flux direction, that is, the quality of the control of the flux and the torque depends on to what extent these parameter values can be known, especially, if the operating speed is low.
Additionally, the estimation of the resistance values during the operation of the motor, which is given by the equations (3) and (4) for the system comprising a speed sensor, or by the equations (3) and (6) for the system comprising no speed sensor, cannot correctly be made in all cases, and is unstable under a particular operating condition and for a particular combination of parameter characteristics of the motor.